What is f(x) = int e^(5x-1)+x dx if f(2) = 3 ?

1 Answer
Jul 6, 2017

f(x)=1/5(e^(5x-1)+5-e^9)

Explanation:

f(x)=int(e^(5x-1)+x)dx" "f(2)=3

now
d/(dx)(e^(5x-1))=5e^(5x-1)

using the chain rule. (This is left as an exercise for the reader to show)

by inspection therefore we have

f(x)=int(e^(5x-1)+x)dx=1/5e^(5x-1)+1/2x^2+C

but f(2)=3

:.3=1/5e^((5xx2-1))+1/2xx2^2+C

3=1/5e^9+2+C

15=e^9+10+5C

:.C=(5-e^9)/5

f(x)=1/5e^(5x-1)+(5-e^9)/5

f(x)=1/5(e^(5x-1)+5-e^9)